A surprisingly upbeat study of a breast-cancer drug had a hedge-fund giant at a crossroads.

It was late July and Robert Atchinson and Phillip Gross—founders of the large but little-known Boston hedge-fund firm Adage Capital Management LP—were up $1 billion in a single day when shares of pharmaceutical company Puma Biotechnology Inc. more than tripled after the release of an encouraging study for the fledgling drug neratinib.